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11-12 Applications
The test functions of the TI
.
80 can be used to build piecewise defined functions.
Define and graph this piecewise defined function.
f(x)=
x
ñ
,
for x≤3
1.5x+1, for 3<x<5
6
ì
x, for x≥5
The
TEST
functions, which return 1 if true and 0 if false, can
be used to build piecewise defined functions. For example,
when x is 4 (x≤3) is false and will return 0.
Follow this procedure to solve the problem.
1. Press
3
and select
FUNC
.
2. Enter the first piece of the function in the
Y=
editor. This
piece is f(x)=x
ñ
for x≤3. It is entered as
(x
ñ
)(x
≤
3)
.
Y
ã
is
then equivalent to x
ñ
×1 for x≤3 and x
ñ
×0 for x>3.
3. Add the second piece of the function in the
Y=
editor. This
piece is f(x)=1.5x+1 for 3<x<5. It is entered as
(1.5x+1)(3
<
x)(x
<
5)
.
When x is less than 3, the test (3<x) returns 0, and the test
(x<5) returns 1. In this case, the second piece of the
function is equivalent to (1.5x+1)×0×1, which is 0. Only
when both of these tests are true will the second piece of
this function be anything but 0.
Graphing a Piecewise Function
Problem
Procedure